For Tegmark, this doesn't really make sense though, since the universe is causal in the same sense that a mathematical model of a dynamical system is causal, and it is spatiotemporal in the same sense that the mathematical concept of Minkowski spacetime is spatiotemporal

I don't think that means that abstract objects in the ordinary sense don't make sense. It just means that he counts a lot of things as concrete that most people might think of as abstract. We don't need a definition of 'mathematical structure' for present purposes, just mathematically precise definitions of 'causal' and 'spatiotemporal'.